A known interferometric instrument is described in the publication by T. Dresel, G. Hausler, H. Vanzke entitled "Three-Dimensional Sensing of Rough Surfaces by Coherence Radar", App. Opt., Vol. 3, No. 7, dated Mar. 1, 1992. This publication proposes an interferometer with a briefly coherent light source and a piezoelectric mirror for sensing rough surfaces. In the measuring instrument, a first beam component in the form of a light wave radiated back from a test object has a second beam component in the form of a reference wave superimposed upon it. The two light waves have a very short coherence length (just a few .mu.m) so that the interference contrast reaches its maximum when the optical path difference is zero. A reflecting element in the form of a piezoelectric mirror is provided for changing the light path of the reference wave. The distance to the test object can be determined by comparing the position of the piezoelectric mirror with the time at which the interference maximum occurs. However, the precise measurement of the interference maximum and its assignment to the light path is relatively complicated.